mat336 - syllabus

### MAT 336 History of Mathematics Spring 2004

Index
Course Description
Syllabus
Homework
Schedule of Presentations

## MAT 336 Syllabus

The texts for MAT 336 will be
• B: The History of Mathematics, an introduction by David Burton (4th Ed.,WCB McGraw-Hill 1999)
• D: William Dunham, Journey through Genius (Wiley 1990, Penguin 1991)
with "documents" chosen from the texts and from:
• S: Dirk Struik, A Source Book in Mathematics, 1200-1800 (Harvard, 1969)

Week 1 (Jan 26) Primitive counting; Positional and non-positional number systems. Mayan calendars. Babylonian number recording. (B: 1.1, 1.3, 2.5)
document VAT 7858 (Berlin Museum; Christian Siebeneicher's website at Bielefeld)
document NBC 7344 (Yale Babylonian Collection; Duncan Melville's website at St. Lawrence University)
document YBC 7289 (Yale Babylonian Collection; Casselman's website at UBC)

Week 2 (Feb 2) The decoding of Plimpton 322. (B: 2.6)
document Plimpton 322 (Columbia Rare Book Collection; David Joyce's website at Clark University, University of Swansea website)
Signup for in-class presentation topics.
Quiz on base-60 and cuneiform numbers.

Week 3 (Feb 9) Egyptian number recording and Arithmetic. (B: 1.2, 2.1, 2.2, 2.3)
document The Rhind Papyrus (St Andrew's website)
Quiz

Week 4 (Feb 16) Thales and Pythagoras; Euclid. (B: 3.1, 3.3, 4.1, 4.2)
document Euclid's calculation of the volume of a cone. (Euclid's Elements website, XII, 10)
Student presentations begin.
Fri. 2/20: Deadline for email of Paper 1 topic.

Quiz

Week 5 (Feb 23) Euclid and Archimedes. (B: 4.3, 4.5)
document Archimedes "On moments" palimpsest.
Student presentations continue.
Quiz

Week 6 (Mar 1) Arab, Indian and Chinese mathematics during the "dark ages." (B: 5.5)
document Table of sines from the Aryabhatiya (Narasimha in Nature Dec 20/27 2001)
document Al-Khwarizmi on quadratic equations (S)
Fri. 2/27 Deadline for detailed outline of Paper 1.
Student presentations continue.
Quiz

Week 7 (Mar 8) Fibonacci; Cardano and Tartaglia. (B: 6.2, 7.2, 7.3)
document Word problems from the 1478 "Treviso Arithmetic" (B)
document Cardano's solution of the cubic (D)
Student presentations continue.

Week 8 (Mar 15) Galileo and Descartes. (B: 8.1, 8.2)
document Descartes on the theory of equations (S)
Fri. 3/19 Paper 1 due.
Student presentations continue.

Week 9 (Mar 22) Newton and Leibnitz. (B: 8.3, 8.4)
document Leibnitz on the Fundamental Theorem of Calculus (S)
Student presentations continue.

Week 10 (Mar 29) Probability: Pascal to Laplace. (B: 9.1, 9.2)
document Pascal on "Pascal's triangle" (S)
Fri. 4/2 Deadline for email of 3-sentence description of Paper 2 topic.
Student presentations continue.
Quiz

Week 11 (Apr 12) Euler and the Bernoullis. (B: 10.2)
document Euler's calculation of the sum of the 1/n2 series (D)
Fri. 4/16 Deadline for detailed outline of Paper 2.
Student presentations continue.
Quiz

Week 12 (Apr 19) Gauss, Bolyai and Lobachevsky (B: 10.3, 11.1, 11.2)
document Gauss' proof of the Fundamental Theorem of Algebra (S)
Student presentations continue.
Quiz

Week 13 (Apr 26) Cantor and the infinite (B: 12.2)
document Cantor on the cardinality of a power set: |P(S)|>|S| (D)
Student presentations continue.
Quiz

Week 14 (May 3) Review
Fri 5/7 Paper 2 due.
Student presentations continue.
Quiz

Anthony Phillips
Math Dept SUNY Stony Brook
tony@math.sunysb.edu
July 9 2004